One of the explosions was at the entrance to a largely Shi'ite Muslim district in the northwest of the capital.
It was the biggest inside the city for months.
This witness believes the government needs to do more to stop the attacks.
"Many people were killed and you can see blood everywhere. They were poor people who were here to earn their living. Why did this happen? Can this corrupt government tell us why? The people are dying because of this government."
Another bomb then detonated in a mostly Sunni district of western Baghdad.
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And in a separate bombing in Sadr City, a vehicle packed with explosives was set off during rush hour, with many of the victims women.
The self-proclaimed Islamic State has claimed responsibility for the Sadr city attack.
This witness is angry at the apparent security failure.
"People here want to make a living, but then bombs go off and kill them. Where are the metal detectors? They say they're searching all the vehicles so how come car bombs keep going off?"
Major General Gary Volesky is a United States commander based in Iraq.
He says, despite the bombings, there are no plans to bring US troops to Baghdad from other locations in the region.
"As we've seen, as the enemy loses more and more terrain they resort to some of these desperate acts. The security forces in Baghdad have the situation under control, but our condolences go out to those families."
Major General Volesky says the protection of forces was the number one priority for the US.
"The Iraqi security forces have not asked us for any assistance frankly, they've got that well in hand, and we have not seen a call to move forces that are currently conducting operations against Daesh (ISIS) in both the Euphrates Valley and the Tigris River Valley back to Baghdad so our assessment is that they are able to handle the issue as they see it."
